Liping Yu , Alex Zunger PHYSICAL REVIEW LETTERS 108, 068701 (2012) Identification of Potential Photovoltaic Absorbers Based on First-Principles Spectroscopic Screening of Materials Liping Yu , Alex Zunger PHYSICAL REVIEW LETTERS 108, 068701 (2012) Kishida Takuto

Contents Ⅰ.Introduction Ⅱ. Discussion & Result Ⅲ. Summary Photovoltaic (PV) absorbers Shockley and Queisser (SQ) limit Ⅱ. Discussion & Result Spectroscopic limited maximum efficiency (SLME) Which materials are good potential PV absorbers. Ⅲ. Summary Ⅳ.Future plan

Photovoltaic (PV) absorbers Ⅰ.Introduction Photovoltaic (PV) absorbers PV absorbers PV absorbers have attracted attention as clean energy for the next generation. Solar energy that reaches the earth in one hour is comparable to the energy humanity consumes in a year.(about 1kW/m2) ⭕ Energy source is the sun. ⭕ CO2 is not emitted. ❌ Conversion efficiency is not high. ❌ Price is high. Classification Silicon series Si : 24.7 % ( Theoretical limitation 29 % ) Solar cell Compound series GaAs : 28.3 % , CIGS : 20.3 % , CdTe : 16.7 % Organic series Dye sensitization : 11.2% , Organic thin film : 7.9 %

Shockley and Queisser (SQ) limit Ⅰ.Introduction Shockley and Queisser (SQ) limit In 1961,Shockley and Queisser offered p-n junction PV absorbers efficiency limit by numerical calculation. Efficiency limit η is expressed as a function of energy gap Eg. SQ limit Efficiency limit is calculated using the ideal value. △Not taking account of direct or indirect gap. △Radiative recombination is the only recombination process. ・ http://kats.issp.u-tokyo.ac.jp/kats/semiconII/note7.pdf

Spectroscopic limited maximum efficiency Ⅰ.Introduction Spectroscopic limited maximum efficiency (SLME) The SLME captures the leading physics of absorption, emission, and recombination characteristics, resolving a spread of different efficiencies for materials having the same gap. (ⅰ) the existence of various energetic sequences of DA, DF and indirect band gaps (ⅱ) the specific shape of the absorption near the threshold (ⅲ) the dependence of radiative recombination losses on the energy separation between the minimum gap Eg and Egda

Ⅱ. Discussion & Result SLME Taking account of direct or indirect gap →Classifying materials into four ‘‘optical types’’(OT1~4) OT1 OT2 OT3 OT4

Comparison of SQ efficiency and SLME Ⅱ. Discussion & Result Comparison of SQ efficiency and SLME The power conversion efficiency of a thin film (L) solar cell depends on the fraction of the radiative electron-hole recombination current (fr) and the photon absorptivity [a(E)] . SQ efficiency Radiative recombination is the only recombination process for all optical types of materials. × nonradiative recombination dominates SLME where k is the Boltzmann constant, T is the temperature, and Δ= Egda – Eg

Comparison of SQ efficiency and SLME Ⅱ. Discussion & Result Comparison of SQ efficiency and SLME For photon absorptivity a(E) SQ efficiency SLME where L is the thickness of the thin film, α(E) is the calculated absorption coefficient from first principles. SLME improves upon the SQ efficiency formula in the description of both fr and a(E)

Calculation method GW approximation （G0W0+HSE06） Ⅱ. Discussion & Result Calculation method GW approximation （G0W0+HSE06） This method has been widely and successfully applied in firstprinciples quasiparticle electronic-structure calculations for many materials. Predicted minimum band gaps for some I-III-VI compounds have an average error of less than 12% with respect to experiments.(L=0.5μm) Ip-IIIq-VIr chalcopyrite group materials I = Li , Na , K , Rb , Cs , Cu , Ag III = B , Al , Ga , In , Tl , Sc , Y VI = O , S , Se , Te

Chalcopyrite materials Ⅱ. Discussion & Result Chalcopyrite materials c a Cu In Se CuInSe2(Ⅰ-Ⅲ-Ⅵ2) Chalcopyrite semiconductor. Experimental energy gap =1.04[eV] (direct gap) Lattice parameter a=5.786[Å] c/a=2.016

GW gaps of 215 compounds For example Ⅱ. Discussion & Result GW gaps of 215 compounds (ⅰ)For OT1, within the same structure type, the band gap of materials decreases with increasing atomic number of one atom when the other two atoms are held fixed. For example (ⅱ)The optical types can change if the stoichiometry changes within the same element set. Cu3TlSe2(OT3)→Cu5TlSe3(OT4) →Cu7TlSe4(OT1)→CuTlSe2(OT2)

GW gaps of 215 compounds (OT2、space group #225) → Eg = 0.07 eV NaTlO2 Ⅱ. Discussion & Result GW gaps of 215 compounds (ⅲ)For the same compound, the minimum band gap (Eg) may vary by more than 2 eV in different crystal structures, whether or not the optical type changes (OT2、space group #225) → Eg = 0.07 eV (OT4、space group #166) → Eg = 2.27 eV NaTlO2 (ⅳ) All reported I3III1VI3 materials have small differences (less than 0.2 eV) between Egdf, Egda, and Eig . (except Li3BO3 which has a 0.43 eV difference between Egda and Edfg. )

SLME for I-III-VI thin film materials Ⅱ. Discussion & Result SLME for I-III-VI thin film materials The SQ efficiency limit depends only on Eg for all optical types , predicting that the best gap for a PV absorber is 1.34 eV, at which ηSQ = 33.7% Around the same Eg, ηSQ depends on the ‘‘optical types’’ and absorption spectra. For example AgInTe2 (OT1) Cu7TlS4 (OT1) CuYTe2(OT3) Eg[eV] 1.17 SLME[%] 27.6 22.6 7.5

Which materials are good potential PV absorbers Ⅱ. Discussion & Result Which materials are good potential PV absorbers There are about 25 materials with SLME higher than 20% . These high-SLME materials have the band gaps ranging from 0.8 to 1.75 eV. 25 materials with high SLME 18 out of 25　→　OT1 , 7 out of 25　→　OT3 None of them have been found to be OT2 or OT4 →OT2 and OT4 materials are least favorable for PV absorbers.

Which materials are good potential PV absorbers Ⅱ. Discussion & Result Which materials are good potential PV absorbers High-SLME materials ( Ip-IIIq-VIr ) CuInSe2 , CuGaSe2 , CuInS2 CuInTe2 , CuGaTe2 , AgInS2 AgInSe2 , AgInTe2 , AgGaSe2 , AgGaTe that have been found experimentally to be reasonable solar absorbers but are much less studied. Most of these previously recognized absorber materials within this group have (1:1:2) stoichiometry. Materials with other stoichiometries also have high SLME. (e.g., AgIn5Se8 , Cs3AlTe3 )

Ⅱ. Discussion & Result Cu-Tl-Ⅵ materials All six high-SLME Cu-Tl-VI materials (four Cu7TlS4 , Cu3TlS2 , Cu3TlSe2) Non-(1:1:2) stoichiometry Contain only Tl of +1 oxidation state Tl is highly toxic → These Tl-containing materials might be disfavored. Tl1+ → Other nontoxic elements in the 1+ oxidation state. Cu-Tl-VI → Cup-IIIq-VIr → Cup-(ⅠⅡ)q-VIr Cup-(ⅠⅡ)q-VIr materials that have SLME more than 20%, not involving Tl. Cu7TlS4 → Cu7(ⅠⅡ) S4 Cup-IIIq-VIr → Cup-(ⅠⅡ)q-VIr Cup-(ⅠⅡ)q-VIr materials that have SLME more than 20%, not involving Tl.

Ⅲ. Summary SLME improves upon the SQ efficiency formula for the initial material screening. SLME considers different optical types and material-dependent nonradiative recombination loss. Testing the idea on a couple of hundred generalized I- III-VI chalcopyrites using first-principles spectroscopy calculations and identifying potential PV absorber materials . → Cup-(ⅠⅡ)q-VIr materials that have SLME more than 20%, not involving Tl that is highly toxic

Ⅳ.Future plan Cu-Tl-VI → Cup-(ⅠⅡ)q-VIr (Tl1+) 2+ 3+ 1+ Cu - Tl - VI Cu3 - ⅠⅡ - VI3 Cu - - VI For example Ⅰ = Na , K Ⅱ = Fe , Mg Cu3 - K Mg - S3